The orthogonal frequency division multiplexing (OFDM) technique has been widely used in the processing of signals. An OFDM circuit provides good bandwidth efficiency and good resistance to multi-path fading channel by means of dividing the full bandwidth into a plurality of small sub-channels. If compared with the technology using coherent bandwidth, the small sub-channels can be viewed as flat fading channels so that one-tap equalizers can be used to recover amplitudes and phases of signals more efficiently. The one-tap frequency-domain equalizer estimates and compensates channel effects with less complexity than time-domain equalizer.
A signal received by an OFDM equalizer is consisted of its signal component and its channel component. The channel component comprises the multi-path channel effects and other channel parameters practically including filter response delay, phase noise, carrier frequency offset and timing offset. In the conventional OFDM systems such as WLAN ETSI 802.11a/g and ETSI HiperLan/2, it is necessary to use known signals as preamble signals to conduct channel estimation and channel compensation, so that the signal component may be recovered. In a short-range communication system, such in the indoor model, the equalization of signals may further take the advantage of the correlation properties of neighboring sub-channels to improve the channel estimation effects.
Signals received by an OFDM equalizer may be expressed by the following equation:Ŷk,l=Xk,l/Ĥk  (1)wherein Xk,l represents the received signals of the lth OFDM symbol at the kth sub-channel, Ŷk,l is its signal component and Ĥk is its channel effect.
The channel effect Ĥk is a complex value and may be expressed by:{circumflex over (H)}k=Ĥre,k+j·Ĥim,k  (2)wherein Ĥre,k is its real value and Ĥim,k is its imaginary value.
As a result, the received signal may be expressed as:Ŷk,l=Xk,l/Ĥk=Xk,l/({circumflex over (H)}re,k+j·Ĥim,k)So we have:
                                          Y            ^                                k            ,            l                          =                                            X                              k                ,                l                                      ⁡                          (                                                                    H                    ^                                                        re                    ,                    k                                                  -                                                      H                    ^                                                        im                    ,                    k                                                              )                                                                          H                ^                                            re                ,                k                            2                        +                                          H                ^                                            im                ,                k                            2                                                          (        3        )            
In order to compensate the channel effect, a complex-valued divider is needed. A circuit to conduct the equalization of the received signals, four real-valued multipliers and two real-valued dividers are deeded for each sub-carrier. Such a circuit is complicated, occupies a larger space and is costly in design and manufacture.